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The butyllithium removes a proton from the relatively acidic alpha carbon. The carbanion attacks the ketone which yields a oxygen anion. The oxygen anion attacks the silicon to form a 4-membered ring which then opens to yield a vinyl silane and a silyl alcohol – a Peterson elimination.
K. Itami, T. Nokami and J. Yoshida, Org. Lett., 2000, 2, 1299–1302.